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Diffusion processes are important models for many real-world
phenomena, such as the spread of disease or rumors. We studied
different aspects of diffusion processes in networks, focusing on
designing efficient distributed algorithms for positive diffusion
processes and good intervention strategies to control harmful
diffusions.

First, we design and analyze various distributed algorithms for
diffusion processes. We want to devise efficient distributed
algorithms, which are easy to implement, to help the spreading of
positive/useful information. We refer to these processes as positive
diffusions. Earlier work has studied this for a variety of models,
mainly based on static networks. The major point that separates our
research with previous work is that we consider dynamically changing
networks, which extends previous models to a larger range of real-life
situations. Depending on the ways that networks are altered, we
studied diffusion processes over the following two types of dynamic
networks: (1) networks are changed due to individuals' decisions or
behaviors; (2) networks are controlled by an adversary.

Secondly, we study how to devise good intervention strategies to
control diffusion processes. This problem is crucial when we deal with
harmful information like human diseases or computer viruses. We refer
to these processes as harmful diffusions. We distinguish between
centralized and decentralized intervention strategies. In centralized
intervention strategies, there is a controller who has a limited
amount of intervention resources (e.g. vaccinations or antidotes in
the case of diseases). We study the problem of allocating these
limited resources among the network agents so that the spread of the
diffusion process is minimized. In decentralized intervention
strategies, each individual in the network makes their own decision on
protecting themselves, based on their individual utility and local
knowledge. In such settings, we are interested in questions such as:
is there a stable set of intervention strategies?  What's the cost of
decentralized solutions compared with an optimal centralized one?
Lastly, we augment our studies of intervention strategies with the
consideration about individual behavior changes which would lead to a
new kind of network dynamics. Earlier work has shown that the
combination of behavior change and intervention failure (e.g. failed
vaccination) can lead to perverse outcomes where less (intervention
resources) is more (effective). However, the extent of the perversity
and its dependence on network structure as well as the precise nature
of the behavior change has remained largely unknown.
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